Thank you, all, for your feedback, especially the discussion on Phil Harland's blog. Here I would just like to offer a couple of clarifications, and possibly point towards some responses to people's comments.
On the whole I agree with Harland - and I did not read his remarks as intending to supply a 'refutation'! I especially agree with the remark that historians should recognize the fact that Jesus and others were regarded as 'miracle workers' (something which I did not deny in my original post). In fact, this acknowledgement leads on to the very question that I wanted to ask, namely, that if we acknowledge that Jesus was regarded as a miracle-worker, why was he thus regarded? To me this seems like a normal historical question, and I was asking why this is 'off-limits' in the case of Jesus. In the case of Alexander of Abonuteichos (mentioned by Harland), for instance, I doubt anyone would deny that he was regarded by some as a miracle worker. And I expect that few historians would refuse to ask why he was regarded as a miracle-worker, on the basis of the limitations of the historical method.
Possible explanations for belief in Jesus as a miracle-worker
When we are faced with the question of why Jesus was regarded as a miracle-worker, there seem to be three main alternatives: the supernatural explanation (that he really was a miracle-worker), the rationalistic (e.g., that he successfully employed basic medical techniques), or the mythical (that Jesus was not actually a miracle-worker and that these stories were attributed to him at a later date for theological reasons). This tripartite division of possible solutions of course derives from Strauss, and the purpose of my original post was not so much to make a new contribution to this discussion as to ask why more recent scholars reintroduce 'miracle' as a category appropriate for talking about Jesus (at least with regards to his reputation), and rarely (if at all) discuss these three candidates for explaining this reputation.
At least two of these explanations (the rationalistic and the mythical) would not seem to be especially controversial as explanations in themselves (even if we would question the plausibility of some 'rationalistic' explanations). I expect that one or the other of these would normally be invoked in discussion of ancient (or even more modern) figures to whom miracles have been attributed - and yet scholars do not frequently invoke either of these explanations in connection with Jesus, but stop with his 'reputation'.
The 'supernatural' explanation and Hume's view
The 'supernatural' explanation would seem to be the most controversial, for the reason that few would regard it in most cases as an adequate historical explanation of a miracle report in the case of most historical figures (though, of course, many believers would regard it as appropriate in the case of Jesus). One reason we might reject the supernatural explanation is Hume's view. As I read Hume, his argument is not circular (or at least it is not obviously so). At the very least, we can state a weaker form of his argument that is not circular:
(1) Supernatural events (like 'miracles', if they occur) do not occur very often (they are 'very unusual'; I hope this is uncontroversial!).
(2) Very unusual events require extremely strong verification, especially if there is an alternative explanation that would require less strong verification.
(3) Therefore, we would need extremely strong verification to assert with justification that a miracle had occurred.
(4) If this extremely strong verification is absent, we should accept a non-supernatural explanation as more probable.
These premises all seem to be quite plausible, and if the argument is circular I do not see where it begs the crucial question. And even if the argument is not true in general terms (so as to rule out a miracle ever verifying that a miracle had occurred), it would surely be valid in the case of ancient texts such as the reports of the miracles of Alexander of Abonuteichos. If it is valid in cases such as this, then if we are treating the Gospels as historians normally treat other historical texts then this judgement should apply to them as well: and therefore we would be obliged to accept a rationalistic or mythical explanation of the origin of Jesus's reputation as a miracle worker.
The option remains open to the reader of the Gospels to reject Hume's argument (and any similar argument) and suggest that Jesus was regarded as a miracle-worker because he was a miracle worker (though I think this would have to be done on theological grounds rather than on any logical charge of circularity). Some scholars do this quite openly - for instance N.T. Wright. But many scholars do not, and instead choose to stop at Jesus's 'reputation' as a miracle-worker without asking the question of why he was so regarded. The purpose of my previous post was to suggest that the history of scholarship has provided us with at least two historically possible explanations of why Jesus was regarded as a miracle-worker (the rationalistic and the mythological), and therefore if some scholars choose not to examine this question they need to do so for reasons other than that it is not an historically proper question, or that an historically proper explanation cannot be provided.